The bond-fermion entanglement entropy for the Kitaev spin chain and honeycomb models are shown in panels (a) and (c). The quantum phase transition is identified by the discrete jump in the entanglement entropy. Using the phase-shifted momenta and the correlation function measurement, the results from the quantum computer now clearly show the phase boundary, even if the magnitude of the jump is reduced. Using this step as the identifying feature, we are able to reconstruct the phase diagram of the two models as a function of both exchange parameters
on the IBM-Almaden quantum computer, as shown in Fig. REF (c) and (d). This efficient identification of the phase boundary relies on the difference of the topology of the single-particle wavefunctions in the two different phases. When \(|J_i|<|J_j+J_k|\)  (with \(i,j,k \in \lbrace x,y,z\rbrace \) ), the single-particle spectrum is gapped, and the ground state of the phase is known as the gapped \(Z_2\)  spin liquid in the sense that it can be mapped to the toric code model [1]}. On the other hand, when \(|J_i|\ge |J_j+J_k|\) , the single-particle spectrum is gapless, and the ground state of the phase is a spinon chiral topological superconductor [2]}. The difference in the single-particle spectrum corresponds to edge modes: if the system were terminated with a boundary, then the spinon chiral topological superconducting phase would support edge modes, while the gapped \(Z_2\)  spin liquid phase would not. The sharp jumps in Fig. REF  are related to the appearance or disappearance of these edge modes in a finite system. This effect is quite robust, even in the presence of noise; it has its origin in the intrinsic topological nature of the quantum system.
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